A343045 -id:A343045 - cp's OEIS frontend

A343044 Array T(n, k), n, k >= 0, read by antidiagonals; lunar addition table for the primorial base.

0, 1, 1, 2, 1, 2, 3, 3, 3, 3, 4, 3, 2, 3, 4, 5, 5, 3, 3, 5, 5, 6, 5, 4, 3, 4, 5, 6, 7, 7, 5, 5, 5, 5, 7, 7, 8, 7, 8, 5, 4, 5, 8, 7, 8, 9, 9, 9, 9, 5, 5, 9, 9, 9, 9, 10, 9, 8, 9, 10, 5, 10, 9, 8, 9, 10, 11, 11, 9, 9, 11, 11, 11, 11, 9, 9, 11, 11, 12, 11, 10, 9, 10, 11, 6, 11, 10, 9, 10, 11, 12

Offset: 0

Rémy Sigrist, Apr 05 2021

The i-th digit of T(n, k) in primorial base is the largest of the i-th digits of n and of k in primorial base.

For n = 0..23, the factorial and primorial base representations of n are the same; hence the date sections for this sequence and for A343040 are the same.

			Array T(n, k) begins:
  n\k|   0   1   2   3   4   5   6   7   8   9  10  11  12
  ---+----------------------------------------------------
    0|   0   1   2   3   4   5   6   7   8   9  10  11  12
    1|   1   1   3   3   5   5   7   7   9   9  11  11  13
    2|   2   3   2   3   4   5   8   9   8   9  10  11  14
    3|   3   3   3   3   5   5   9   9   9   9  11  11  15
    4|   4   5   4   5   4   5  10  11  10  11  10  11  16
    5|   5   5   5   5   5   5  11  11  11  11  11  11  17
    6|   6   7   8   9  10  11   6   7   8   9  10  11  12
    7|   7   7   9   9  11  11   7   7   9   9  11  11  13
    8|   8   9   8   9  10  11   8   9   8   9  10  11  14
    9|   9   9   9   9  11  11   9   9   9   9  11  11  15
   10|  10  11  10  11  10  11  10  11  10  11  10  11  16
   11|  11  11  11  11  11  11  11  11  11  11  11  11  17
   12|  12  13  14  15  16  17  12  13  14  15  16  17  12

Rémy Sigrist, Table of n, a(n) for n = 0..10010
Rémy Sigrist, Colored representation of the array for n, k < 2*3*5*7*11 (where the color is function of T(n, k))
Rémy Sigrist, PARI program for A343044
Index entries for sequences related to dismal (or lunar) arithmetic
Index entries for sequences related to primorial base

Cf. A087061, A235168, A343040, A343045.

PARI
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See Links section.
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A343041 a(0) = 0 and for any n > 0, a(n) = A343040(a(n-1), n).

Original entry on oeis.org

0, 1, 3, 3, 5, 5, 11, 11, 11, 11, 11, 11, 17, 17, 17, 17, 17, 17, 23, 23, 23, 23, 23, 23, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 71, 71, 71, 71, 71, 71, 71, 71, 71, 71, 71, 71, 71, 71, 71, 71, 71, 71, 71

Offset: 0

Rémy Sigrist, Apr 03 2021

This sequence has similarities with A087052.
If we remove duplicate terms, then we obtain A200748.
The value A200748(k) appears A130493(k) times for any k > 0.

			The first terms, in decimal and in factorial base, are:
  n   a(n)  fact(n)  fact(a(n))
  --  ----  -------  ----------
   0     0        0           0
   1     1        1           1
   2     3       10          11
   3     3       11          11
   4     5       20          21
   5     5       21          21
   6    11      100         121
   7    11      101         121
   8    11      110         121
   9    11      111         121
  10    11      120         121
  11    11      121         121
  12    17      200         221
  13    17      201         221
  14    17      210         221

Rémy Sigrist, Table of n, a(n) for n = 0..5039
Rémy Sigrist, PARI program for A343041
Index entries for sequences related to dismal (or lunar) arithmetic
Index entries for sequences related to factorial base representation

Cf. A087052, A130493, A200748, A343040, A343045.

PARI
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See Links section.
```

cp's OEIS Frontend

A343044 Array T(n, k), n, k >= 0, read by antidiagonals; lunar addition table for the primorial base.

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